Karen K.

# If there a formula for solving time related questions???????????????????????????????????????

It takes Sarah 5 hours to complete a task and it takes Ben 4 hours to complete the same task. If Sarah and Ben work together, and Ben leaves after 2 hours, how much longer must Sarah work to complete the task on her own (in hrs)?

## 2 Answers By Expert Tutors

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Tutor
5.0 (345)

I love math, and love to teach it

Karen K.

Thanks Steven.  It's very simple when you put it like that.

A variation of this question, if asked how long it would take to complete the job if they worked together the whole time, how would you do it?
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04/21/14 Steven B.

tutor

RSTS + RBTB = J

(1/5)TS + (1/4)TB = 1   Substitute for rates and job.

Note that since they both start and stop at the same time, TS = TB, so substituting we get:

(1/5)TS + (1/4)(TS) = 1

At this point there are several approaches to finding the answer but since I am not fond of dealing with fraction, I can multiply all terms by the common denominator (20) to get rid of them.

20[(1/5)TS + (1/4)(TS]) = 20(1)

4TS + 5TS = 20      Distribute (and simplify)

9TS = 20                Adding (since they are both TS)

Then divide both sides by 9

9TS = 20
9       9

TS = 20/9 and since TB = TS, TB = 20/9

20/9 = 22.2222222...

The basic formula works for a lot things, and you'll notice a change in variable name only.  If you are doing distance (RT = D, rate x time = distance) or mixture (PQ = S, where P = %, Q = Quantity and S = Solution, although this one is a little more complicated than that).  Often you will need to write 2 (or more) equation that can then be manipulated and combined (usually by substitution) to arrive at one equation in one variable (for example, in the 2nd problem, the 1st two equations are added together and then we had to write a third equation TB = TS in order to substitute and arrive at a new equation with just one variable in it).
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04/24/14 Steven B.

tutor
I wrote an answer to your second question but apparently it didn't save correctly.  I'll type it in again tomorrow.  WAY past my bedtime now.
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04/24/14 Steven B.

tutor
You use the same formula [In fact this formula is similar to the "other" distance formula RT = D where R = Rate, T = Time and D = Distance.  And the mixture formula P1Q1 + P2Q2 = P3(Q1 + Q2)].  Anyway...

RSTS + RBTB = J    Starting from here...

(1/5)TS + (1/4)TB = (1)    Now we have a problem, because we have one equation with 2 variables in it

If only I could find another equation!  Ah Ha!  Since they both worked the same amount of time, TS = TB.

(1/5)TS + (1/4)TS = (1)    Substituting TS for TB.

At this point there are several approaches one can use to simplify the equation, but I don't like to have to deal with fractions, so I am going to multiply by the LCD (least common denominator), which is 20, to get rid of them.

20[(1/5)TS + (1/4)TS] = 20(1)     x20  which gives us...

4TS + 5TS = 20     Next we add the like terms...

9TS = 20     Now dividing both sides by 9

TS = 20/9 = 2 & 2/9 hrs. or 2.2222... hrs. or ≈ 2.22 hrs. (or 2 hour 13 & 1/3... min., etc. etc. etc.)

And finally if TS = 20/9 then TB = 20/9
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04/24/14 Tutor
4.8 (4)

Mathematics professor at Community Colleges Steven B.

tutor
Sorry, this solution only works if they both worked the same amount of time.  Read questions more carefully.  Better no answer than the wrong answer.
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04/21/14 Parviz F.

No. It works well.
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04/21/14 Steven B.

tutor
"If Sarah and Ben work together, and Ben leaves after 2 hours, how much longer must Sarah work to complete the task on her own (in hrs)?"

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04/21/14 Steven B.

tutor
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04/21/14 Steven B.

tutor
Not to mention the fact that the student asked "Is there a formula for solving time related questions."  Not how do solve this particular problem.  Teach a child to fish . . .
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04/21/14 Parviz F.

I give the formula, and let the students work to solve for X.
Copying all the work does not help.

It is just like distributing x amount of work to the ratio of 4 and 5

1/ 4 + 1/5 =1/x

9   =
20      X

X = 20/ 9 = 2. 22 hrs

1/4 of a job with first worker + 1/ 5 of job done by second worker adds up that if both work together it will take 2. 22 hrs to complete the task.
YOU CAN FIND  THIS PROBLEM IN EVERY ALGEBRA BOOK , I SUGGEST LOOK UP ONE BEFORE GIVING YOUR COMMENTS.
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04/21/14 Steven B.

tutor
I hope you are not a tutor
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04/21/14 Steven B.

tutor
or teacher.  and you STILL have NOT read the question!  It is not asking how long it takes for both of them to finish the task together, but how much longer it takes Sarah to finish if Ben only works for 2 hours. READ THE QUESTION BEFORE YOU ANSWER THE QUESTION!!!
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04/21/14 Steven B.

tutor
You can lead a horse to water. . .
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04/21/14

Karen K.

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04/21/14 Parviz F.

OK Steve:
If they work together it will take 2.22 hrs to finish the job.

If one quits after 2 hours, then only 0.22 hr of job is left for one to finish singlehandedly.

Keep on hoping and I will give my best wishes to you.

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04/21/14 Parviz F.

So:
0.22    = X
2.22       5

X = 5 ( 0.22) / 2.22 = 0.495495495 ≈0.5

So your  MagnificentAnswer of 0.5 hr that Sarah has to work singlehandedly can be achieved.

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04/21/14 Steven B.

tutor
Right AND wrong.  If they both work together it IS 2.22... hours AS I said.  but it is not 0.45... it is exactly .5 hours.  I am sorry that you are not right on this.  I really am.
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04/24/14 Steven B.

tutor
OH MY GOSH!  You are a mathematics teacher at "several colleges".  I am sorry but your math skills couldn't get you job at a high school.  I am calling you out on the "several colleges" bit.  Prove it!  Which ones and under what name and what subject(s).  And while you are busy proving things, find me a source: book, publisher, edition and page where I can find you equation "1/ 4 + 1/5 = 1/x...YOU CAN FIND THIS PROBLEM IN EVERY ALGEBRA BOOK, I SUGGEST LOOK UP ONE BEFORE GIVING YOUR COMMENTS".
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04/24/14 Parviz F.

Just look in a word problems , where a job is done by one worker in 4 hours, and other by 5 hours, then if they work together , how long will it take to finish the job.
Which was calculated here it was found by using the formula
1/4 + 1/5 = 1/x

X = 2.22
Now problem asks if one quits after 2 hours, then how long will it take for the other to finish the job:

We see that only 0.22 hours of work will be left to finish

0.22  = X
2. 22     5

it says that 0.22hr of 2 .22 hr what fraction of 5 hours., and make the ratio above.
X = 0.5

Job finishes after 2.5 hours for given scenario.

No more communique will be responded.

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04/24/14

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